What is a Cosmological Constant?

Einstein first proposed the cosmological constant (not to be confused with the Hubble
Constant) usually symbolized by the greek letter "lambda" (Λ), as a mathematical fix to the theory of general relativity.
In its simplest form, general relativity predicted that the universe must either expand or
contract. Einstein thought the universe was static, so he added this new term to stop the
expansion. Friedmann, a Russian mathematician, realized that this was an unstable fix,
like balancing a pencil on its point, and proposed an expanding universe model, now called
the Big Bang theory. When Hubble's study of nearby galaxies
showed that the universe was in fact expanding, Einstein
regretted modifying his elegant theory and viewed the cosmological constant term as his
"greatest mistake".

Many cosmologists advocate reviving the cosmological constant term on theoretical
grounds. Modern field theory associates this term with the energy density of the vacuum.
For this energy density to be comparable to other forms of matter in the universe, it
would require new physics: the addition of a cosmological constant term has profound
implications for particle physics and our understanding of the fundamental forces of
nature.

The main attraction of the cosmological constant term is that it significantly improves
the agreement between theory and observation. The most spectacular example of this is the
recent effort to measure how much the expansion of the universe has changed in the last
few billion years. Generically, the gravitational pull exerted by the matter in the
universe slows the expansion imparted by the Big Bang. Very recently it has become
practical for astronomers to observe very bright rare stars called supernova in an effort
to measure how much the universal expansion has slowed over the last few billion years.
Surprisingly, the results of these observations indicate that the universal expansion is
speeding up, or accelerating! While these results should be considered preliminary, they
raise the possibility that the universe contains a bizarre form of matter or energy that
is, in effect, gravitationally repulsive. The cosmological constant is an example of this
type of energy. Much work remains to elucidate this mystery!

There are a number of other observations that are suggestive of the need for a
cosmological constant. For example, if the cosmological constant today comprises most of
the energy density of the universe, then the extrapolated
age of the universe is much larger than it would be without
such a term, which helps avoid the dilemma that the extrapolated age of the universe is
younger than some of the oldest stars we observe! A cosmological constant term added to
the standard model Big Bang theory leads to a model that appears to be consistent with the observed
large-scale distribution of galaxies and clusters, with
WMAP's measurements of cosmic microwave background fluctuations, and with the
observed properties of X-ray clusters.

WMAP and the Cosmological Constant

By characterizing the detailed structure of the cosmic microwave background
fluctuations, WMAP is able to accurately determine
the basic cosmological parameters, including the
cosmological constant, to better than 1% (as of the year 2013).

Further Reading:

Donald Goldsmith, "Einstein's Greatest Blunder? The Cosmological Constant and
Other Fudge Factors in the Physics of the Universe", (Harvard University Press:
Cambridge, Mass.) A well written, popular account of the cosmological constant and the
current state of cosmology.